Python Keep points in spline interpolation

Question

I wrote a code that performs a spline interpolation:

x1 = [ 0., 13.99576991, 27.99153981, 41.98730972, 55.98307963, 69.97884954, 83.97461944, 97.97038935, 111.9661593, 125.9619292, 139.9576991, 153.953469 ]
y1 = [ 1., 0.88675318, 0.67899118, 0.50012243, 0.35737022, 0.27081293, 0.18486778, 0.11043095, 0.08582272, 0.04946131, 0.04285015, 0.02901567]

x = np.array(x1) 
y = np.array(y1)

# Interpolate the data using a cubic spline to "new_length" samples
new_length = 50
new_x = np.linspace(x.min(), x.max(), new_length)
new_y = sp.interpolate.interp1d(x, y, kind='cubic')(new_x)

But in the new dataset generated new_x and new_y the original points are eliminated, only the first and the last values are kept. I would like to keep the original points.

Answer 1

Right, linspace won't generate any of the values in x except the ones you pass to it (x.min() and x.max()).

I don't have a great snappy answer, but here is one way to do it:

# Interpolate the data using a cubic spline to "new_length" samples
new_length = 50
interpolated_x = np.linspace(x.min(), x.max(), new_length - len(x) + 2)
new_x = np.sort(np.append(interpolated_x, x[1:-1]))  # include the original points
new_y = sp.interpolate.interp1d(x, y, kind='cubic')(new_x)

This code uses:

• np.linspace to create as many extra points as we need
• np.append to combine the array of extra points with the original points from x
• np.sort to put the combined array in order